样本量为2的极小样本相容性检验方法

在航空航天领域由于成本、时间周期等原因进行疲劳寿命及可靠性评估时样本量通常极少（m=1或2），利用相容性检验方法可对样本量进行扩充。常规的Wilcoxon秩和检验和K-S（Kolmogorov-Smirnov）检验适用于小样本情形，而极小样本相容性检验方面研究较少，且缺乏对方法合理性的详细说明和对不同方法检验功效优劣的比较。航空航天产品疲劳寿命多服从正态分布，因此本文主要以正态分布作为研究对象。利用Monte Carlo仿真发现从某一正态分布N（μ，σ²）中随机抽取两个样本x₁、x₂计算均值μ₁和标准差σ₁后构建新正态分布N（μ₁，σ₁²），其±σ₁、±2σ₁和±3σ₁范围内的点落在原正态分布N（μ，σ²）±3σ范围内的概率依次为99.80%、98.13%和97.37%。在此基础上针对现场试验数据样本量为2的情况，本文提出利用3σ原则对先验信息数据进行相容性检验从而扩充样本量的方法。将该方法与两种文献方法对比后发现其误差率明显更低并呈现出检验性能随先验数据增加而不断提高的优势。

Compatibility test method in minimal samples situation with two samples

When evaluating the fatigue life and reliability in the aerospace field, the locale test data sample size is usually extremely small (m=1 or 2) due to the cost and time limits. The compatibility test method can be used to expand the sample size. Conventional Wilcoxon rank sum test method and K-S (Kolmogorov-Smirnov) method are applicable for situation of small sample size. Less research has been conducted on the method for compatibility test of minimum sample size, and there is a lack of detailed explanation of the rationality of the method and comparison of actual effects of different methods. The fatigue life of aerospace products usually obeys the normal distribution, so normal distribution is analyzed in this paper. Two points x₁,x₂ are randomly selected from a normal distribution N(μ,σ²), and the mean μ₁ and standard deviation σ₁ are calculated to construct the new normal distribution N(μ₁,σ₁²). It is found using the Monte Carlo simulation that the probabilities that points placing at ±σ₁, ±2σ₁ and ±3σ₁ ranges of the new normal distribution N(μ₁,σ₁²) place at ±3σ range of the original normal distribution N(μ,σ²) are 99.80%,98.13% and 97.39% respectively. Aiming at the situation that the population follows normal distribution and the sample size is 2, this paper proposes to use the 3σ principle to test the prior information data and thus to expand the sample size. A comparison with other two methods shows that with the proposed method, the error rate is obviously lowered, and with the increase of prior information data, the method performs better.